Once upon a time, Memphis, Tennessee, required bicycle licenses. This was my aunt’s, issued in 1949, when she was ten years old. She rode a J. C. Higgins. The license cost 50 cents. They used the wrong name. My aunt’s name was Claire, not Claira.
For the record, I am very against requiring any sort of licenses or fees for cycling. Cycling is a public good because it relieves congestion and damage to the roads. There shouldn’t be any barriers to riding your bike. If you do own a bicycle it’s a good idea to register it to help you recover it if stolen. I recommend BikeIndex.org, a free registration service.